The best pattern is one where all of the available pellets are evenly spaced to fill the entire pattern...in a perfect world.
Folks most often sell choke tubes for density and distance reasons....and good marketing.
Many times they are sold because we humans dither over what is best and seek to blame anything mechanical for issues with target or bird.
A pattern does open with less choke if you mean more room between each pellet...perhaps the issue is the different definitions of a pattern.
For me, it is the standard 30" and true width often is irrelevant based upon a lack of pellet density.
A standard is important if one is to truely compare one factor to another.
Otherwise, it is all guess by gosh.
For woodcock, shot closer than many birds, a 22"-24" pattern at shot taken distance for evaluation seems to offer the best chance at the little bogsucker and is useful for comparisons.
As far as moving pellets in an efficient manner, the quick thought would be to open the choke but IME, that was seldom useful or dependable to an appreciable degree.
Seems as if it would be so...but no.
A better way is thru either pellet hardness, wad choice or powder burn rate as possibly the top three.
Remember the idea is to move pellets into the annular ring and not out of the pattern.
Most folks do not and it sounds as if you have patterned very little or to a less than optimal degree, procedure-wise.
Just as well, there are other more important things to do and the minutae can get addicting.
You will not find many Registered Trapshooters shooting less than full choke.
Some, I did, shot IM at the 16 but often preferred XF for what it indicated when I shot.
Certainly, Handicap is a Full choke game.
That was an odd comment re Trap, N.
One can break many targets from the 16 with many degrees of choke...average break distance from the 16 is only 32 yards.
But 16 yards targets is not all of Trapshooting or the end all for practicing to shoot Registered Trap.
Perhaps here the difference is between being a Trapshooter...and shooting targets on a trap field.